Another monodromy invariant fundamental solution of this Fuchsian system was constructed
in [1]} by using the \(W\)  conformal field theory. The corresponding tau function
was expressed as a Fourier transform of the semi-degenerate \(W_N\)  conformal block
with the central charge \(c=N-1\) . Hence, by the uniqueness of a fundamental system of a Fuchsian system, \(W\)  conformal blocks are equal to 4d Nekrasov functions. We note that in what follows, we assume convergence of 5d Nekrasov partition functions, and moreover, Fourier transforms of them. Analyticity of 5d Nekrasov partition functions in cases different from our case
was discussed in [2]}.
